Buncho items are easy to spot, which is good news for
you. Once you see an item loaded with variables, numbers, and equations/inequalities,
use the following step method to tackle it:

Step 1: Look at the stem and determine which variable
or term the item wants solved. Circle it.

Step 2: Look at the equation(s) and locate that same
variable or term. Circle it as well. If the entire term isn’t present,
isolate the variable needed to find the right answer.

Step 3: Write out the equation and start manipulating
it—add, subtract, multiply, divide, square, take the square root
of, whatever—until the circled variable or term is isolated on one
side of the equation.

The reason we use the phrase variable or term is
because the SAT often does not ask for the single numerical value
of one variable. It often asks for two variables together or for
one variable with some work done to it. In other words, an item
won’t ask you the value of x. Instead, it will
want the value of 5x. It does this to trip up students
who find what x is, then look down at the answer
choices and pick that value. They get the value of x correct,
but they get the item wrong because it was asking for 5x.

Buncho in Slow Motion

Now that you know the three steps to tackling Buncho items,
we’re going to take you through it in slow motion to demonstrate
exactly how it works.

4.

If , then what is the value of ?

(A)

378

(B)

243

(C)

3

(D)

(E)

1.92

Step 1: Look at the stem and determine which variable
or term the item wants solved. Circle it.

In this case, you want to circle the term .
That’s what the item wants, not x. Sometimes the
test-makers do this solely to bust your chops. Other times, however,
the unusual term (such as ) can provide a
shortcut to answering the item.

Step 2: Look at the equation(s) and locate that same variable
or term. If possible, circle it as well. If the entire term isn’t
present, isolate the variable needed to find the right answer.

In this case, the equation does
not have lurking within it. However, you
should see quite clearly that the key to this item centers on finding
out the value of x.

Step 3: Write out the equation and start manipulating
it, until the circled variable or term is isolated on one side of
the equation.

Here’s where things get interesting. You can solve
for x like we do below, then determine what will
be. The toughest step is realizing that .
This illustrates how the new SAT is all about using exponents and
other lesser known math functions to make things difficult. Now solve:

That gives you x, which you could
then place into and come up with the
correct answer. However, the strange term does
provide a shortcut. Look at the second line of the equation above, .
The term is 14 times less than ,
the thing we are looking for. So if we multiply both sides of the
equation by 14 at that point, we find the answer we are looking
for.

There’s your answer. There is no coincidence at all about
the presence of this shortcut. It gives you an option if you encounter
a Buncho item that does not come out and ask for a single variable.
It means you can either solve for a needed variable or you can do
a little tinkering with the equation and maybe find a shortcut to
the correct answer. Either way, you end up with answer A.

Guided Practice

Try this one on your own:

2.

In
the equation , what is the value
of x?

(A)

–1

(B)

3

(C)

5

(D)

9

(E)

20

Step 1: Look at the stem and determine which variable
or term the item wants solved. Circle it.

This item is a little more straightforward. Circling it
helps you stay focused.

Step 2: Look at the equation(s) and locate that same variable
or term. Circle it as well. If the entire term isn’t present, isolate
the variable needed to find the right answer.

The variable is standing alone amidst a sea of numbers.

Step 3: Write out the equation and start manipulating,
until the circled variable or term is isolated on one side of the
equation.

If you get rid of the 3 first, you won’t have to distribute
this equation.

Guided Practice: Explanation

Step 1: Look at the stem and determine which variable
or term the item wants solved. Circle it.

Circling the x at the end of the stem
is simple enough. It also alerts you to the fact that there’ll be
no shortcut or hijinks on this item.

Step 2: Look at the equation(s) and locate that same variable
or term. Circle it as well. If the entire term isn’t present, isolate
the variable needed to find the right answer.

Because there’s only one variable, x,
circling it in the equation should give you an idea of what you
need to do to isolate it. The 3 needs to go, then the 12, and finally
the 4 right next to it.

Step 3: Write out the equation and start manipulating,
until the circled variable or term is isolated on one side of the
equation.

Time to do some math. Write it all out so you don’t miss
a step:

Fill in answer C and yell out, “Buncho!”

Independent Practice

After you complete the following item, look at the following
page for the explanation.

10.

Let x =
2y. For what value of z is ?

(A)

x

(B)

y

(C)

3

(D)

27

(E)

81

Independent Practice: Explanation

Step 1: Look at the stem and determine which variable
or term the item wants solved. Circle it.

The item is asking you to solve for the value of z.

Step 2: Look at the equation(s) and locate that same variable
or term. Circle it as well. If the entire term isn’t present, isolate
the variable needed to find the right answer.

The z in the equation is attached to y3,
so you know you’ll eventually have to get rid of the y3.
But first you have to do some fancy footwork with the x and
the y.

Step 3: Write out the equation and start manipulating,
until the circled term is isolated on one side of the equation.

You’re dealing with three variables here, which is a lot
to handle. Ideally, you want to get rid of one of those variables.
We know that x = 2y, so why not
change the x in our equation into a y term:

Much better. Now you’re left with just some pretty basic
math:

How about that? The y3 cancels
out, and you end up with 27 = z, answer D.